In this thesis, we discuss multiple-input and multiple-output (MIMO) antenna technology, which can enhance the throughput performance of downlink cellular systems without using more bandwidth and more power. MIMO can improve spectral efficiency with respect to number of the equipped multiple antennas. This paper focus on a fundamental limit of a single user MIMO (SU-MIMO) system in cellular downlink systems, which recently requires high rate throughput for high quality multimedia mobile services. The fundamental limit of a SU-MIMO system is that in the downlink cellular system, the performance of MIMO is limited by the number of multiple receiver antennas at the mobile terminals although the number of multiple transmit antennas at the base station is large. It is impractical for hand-held